There is an important literature on time varying reproduction numbers applied in various epidemics, see for example [1]}, [2]}.
A Bayesian framework for estimating time-varying reproduction numbers was proposed by [1]}, and applied to the SARS epidemic.
In [4]}
a time varying reproduction number is defined as the ratio of the number \(C(t)\)  of infected in day \(t\)  over \(\sum _k w(k) C(T-k)\) , where \(w(\cdot )\)  is the distribution of the generation time of Covid-19, which is often set to be a gamma distribution with mean and standard deviation estimated from specific studies [5]}.
There is a very successful R-package implementing this Bayesian method, called EpiEstim [6]}. We include a comparison between EpiEstim and our approach based on only one of the data sources.
